Calculate the meridional arc (S):
S = A'lat - B'sin(2lat) + C'sin(4lat) - D'sin(6lat) + E'sin(8lat), where lat is in radians.
Definitions:
A' = a[1 - n + (5/4)(n2 - n3) + (81/64)(n4 - n5) ...]
B' = (3 tan/2)[1 - n + (7/8)(n2 - n3) + (55/64)(n4 - n5) ...]
C' = (15 tan2/16)[1 - n + (3/4)(n2 - n3) ...]
D' = (35 tan3/48)[1 - n + (11/16)(n2 - n3) ...]
E' = (315 tan4/512)[1 - n ...]
Calculate the latitude (northing).
y = northing = K1 + K2p2 + K3p4
Definitions: (all angles are in radians)
K1 = Sk0
K2 = k0 nu sin(lat)cos(lat)/2 = k0 nu sin(2 lat)/4
K3 = [k0 nu sin(lat)cos3(lat)/24][(5 - tan2(lat) + 9e'2cos2(lat) + 4e'4cos4(lat)]
nu = a/(1-e2sin2(lat))1/2
p = (long-long0)
k0 = 0.9996
long = longitude of point
lat = latitude of point
long0 = central meridian of the zone
Interpreting the results. In the Northern Hemisphere, the latitude converted to a UTM coordinate tells how far north of the equator (in meters) the point location lies. For latitudes in the Southern Hemisphere, the UTM coordinate tells how far north of the south pole the point location lies.
Using a converter program. For changing latitude and longitude into UTM coordinates, use the converter found in Resources below. Enter the latitude and longitude in degrees decimal and you will find the exact location to with a square meter. Note that if you enter a latitude of "0" (the equator), the corresponding UTM value will be "0."
